A string fixed at both ends oscillates in a standing wave as shown with a wavelength of 400 mm.


What is the length of the string?

  A 50 cm string that is fixed at both ends produces a standing wave in the third harmonic. The speed of the wave on the string is$200\,ms^{−1}$
What is the frequency of oscillation?

  1.Discuss the differences between traveling waves and standing waves
2.A 45cm guitar string fixed at both ends is raised and released so that it vibrates at its fundamental mode. The midpoint of the string passes through its equilibrium position 475 times in one second. Estimate the speed of the wave on the string.v=   $m\,s^{-1}$
3.The guitar string is now gently touched 15cm from one end such that a node is created at that point, but the entire length of the string still oscillates. Calculate the frequency of the sound generated.

  A loudspeaker is placed near the open end of a tube which is closed at the other end.




The length of the tube is 0.45 m and the speed of the sound wave in the air is $340\,ms^{−1}$.

(1)Identify with ticks [✓] the properties of the standing waves and travelling waves.

Standing WavesTravelling Waves
All particles vibrate with the same amplitude
Particles one wavelength apart vibrate in the same phase
Energy is not transferred along the wave

(2)Waves are also classified as transverse and longitudinal. Explain why longitudinal waves are generated by the speaker.
(3)Show that the lowest frequency of a sound wave that will form a standing wave in the tube is approximately 190 Hz.$F$=   Hz
2.In a school concert, two coherent loudspeakers are used in an open area. A student suggests that the quality of the sound that different spectators hear will be affected due to interference. Explain how the interference of sound waves can affect the quality of the sound.

  A thin tube with a length of L is immersed in water and fixed to the base of a container of liquid by a string. The length of the tube above the surface of the water is X and inside the water is Y.



A speaker is emitting a single-frequency sound above the tube. For particular values of X, a standing wave is established in the tube.

1.Explain how a standing wave is formed in this tube.
2.The frequency of the sound is 200 Hz. It is found that the smallest value of X for which a standing wave is established in the tube is 42.0 cm. Estimate the speed of sound in the tube. v=   $ms^{-1}$
3.The string is cut and the tube rises in the container, decreasing the length of tube Y inside the water. When Y is 22cm, the second harmonic of the standing wave is formed. Calculate the total length of the tube.L=   m

  1.A student investigates standing waves in strings. A string is connected to an oscillator where a function generator can adjust the frequency. The other end of the string passes through a pulley and supports a mass.





The student varied the mass $m$ and recorded the values for frequency $f$ for which the first harmonic wass visible on the string. The following graph shows the recorded data.




(2)By referring to the plotted data, explain why it cannot be stated that frequency is directly proportional to mass.

1.An engineer designs a bridge. By using software, they simulate how the amplitude A of the vibration of the bridge varies with the driving frequency $f$ of vibration due to wind.



To avoid resonance, they decided to increase the amount of damping by changing the design of the bridge.
（1）State the difference between forced and free vibrations.
（2）Explain why resonance is dangerous for bridges.
（3）On the graph below, sketch the variation of the amplitude of the vibration of the bridge with the frequency of the forced vibration after the damping is increased.
There is no need to add values to the axes

Dashed lines are showing the graph before the damping is increased
（4）In some cases, resonance can be useful. Describe a practical application of resonance.
2.A restaurant uses a swinging door to provide a convenient way for people to move in and out.

  A taut string on a guitar is fixen)/g5en2 +t tfckk keutr6(k5 d+sa1hd at both ends.
What is $\frac{wavelength of fourth harmonic​}{wavelength of second harmonic
}$for the string?

  A student blows across f/ e29heou8xgf:y zeag m(/ xyq:21vpthe open end of a narrow cylinder which is closed at the other end. If the length of the cylindem/yfoe:19q y 8 huzg(2ev/x2afe:pxgr is 15.0 cm and the speed of sound is $340\,ms^{−1}$, What is the frequency of the wave at the third harmonic?

  A loudspeaker producing sound of a single frequency is placed at a distance $1.5\,m$ in front of a barrier as shown in the diagram.

1.Describe the conditions for which standing waves occur.
2.(1)A microphone moves in a horizontal direction from the barrier to the speaker. The microphone detects loud sound at some positions while at others it detects low intensity sound. Explain why this happens.
(2)The microphone detects three positions of high intensity sound. On the axes given, sketch the relationship between the amplitude of oscillation of the air particles and the distance from the wall.

(3)The distance between two successive loud sound positions is 0.60 m. Calculate the frequency of the sound produced by the loudspeaker. The speed of sound in air is $340\,ms^{−1}$. $f$=   Hz
3.The microphone is placed at the location where the sound is loudest. The barrier is then moved towards the loudspeaker until the sound at the microphone has become quiet. Calculate the distance the barrier has moved. Distance moved   m

  For an open pipe, the frequency of the first harmonic is $f$ and its wavelength is $λ$.
For a given harmonic of the same pipe, the ranges of motion of the particles in the pipe are shown below.


Three statements about the standing wave shown in this pipe are
I.The frequency is $2f$
II.The wavelength is $\frac{λ}{4}$​
III. The wavelength is less than λ
Which statements are true?

  A speaker produces a sound near a pipe that is closed at one end by a movable piston. The piston is moved in the shown direction until a sound is first heard from the pipe. At this time, the length of the part of the tube near the speaker is L.




What is the distance moved by the piston to hear the next resonant sound from the pipe?

  A tuning fork is held above a hollow pipe which is in a long cylfv+ 4stg x8/i 0a-gjuuinder filled with water as shown in the dugf /-ia4x8t j+0 ugsviagram below.
Initially, the pipe is fully immersed in the water. The pipe and the vibrating tuning fork are slowly lifted upward from the surface of the water, creating an air column inside the pipe above the water surface.
A maximum intensity of the sound is first heard when the air column reaches a length $a$ and again at length $b$.


Which of the following statements are correct about the lengths $a$ and $b$, and the wavelength λ?
I.$b=3a$
II.$ λ=\frac{3b}{4}$
III.$ λ=4a$

  The string X of lengtha, ;prvyb*tq4 $L_X$​ has two fixed ends. The string Y of length $L_Y$​ has one free end and one fixed end. Waves travel at the same speed in both strings.
The frequency of the third harmonic of both strings is the same. What is $\frac{​L_X}{L_Y}​​$?

  A pipe of length $L_1$​ is open at one end and closed at the other. It has a first harmonic frequency equal to that of the third harmonic frequency in a pipe with length $L_2$​ that is closed at both ends.
What is the ratio $\frac{L_1}{L_2}$​​?

  A first harmonic standing wave in a pipe that is opened at one end and closed at the other has a period of 5 ms. For a pipe of the same length that is closed at both ends, what is the frequency of the first harmonic?

  A speaker emits sound towards a tube that is open at both ends as shown in Figure A. The speed of sound is $340\,ms^{−1}$ and a standing wave is formed in the pipe. At a particular instant, the positions of particles X and Y are shown.
Figure B shows the displacement of molecules of air in the pipe at this instant in time. Displacement to the right is positive.


1.（1）Explain whether particle X is in the center of a compression or a rarefaction.
（2）On Figure A, use $Y'$ to mark the equilibrium position of particle Y.
2.When the frequency of the sound is increased by 120Hz the next harmonic of the standing wave is formed in the pipe. Show that the length of the pipe is $142\,cm$.L≈   cm

  In an experiment to determine the speed of sound in air, some students used a number of tuning forks of known frequencies and a tube with a moveable piston arranged as shown below.
For each tuning fork they used the setup shown in the diagram.


The students would sound the tuning fork, then move the piston slowly downwards until a loud sound is first heard. The length L was then measured. This was repeated for different tuning forks.
The graph shows the variation of $\frac{1}{L}$​ with frequency.

1.Draw the line of best fit.
2.Calculate the fractional uncertainty of $\frac{1}{L}$ when the length is 20 cm.Fractional uncertainty =  
3.(1)Determine the gradient, expressing your answer with the correct SI units.
(2)Use the gradient calculated in (i) to determine the speed of sound.v=   $ms^{-1}$