A collection of problems on standing waves

Question 1

A string of length L is clamped at each end and vibrates in a standing wave pattern. The wavelengths of the constituent traveling waves cannot be:

  1. L/2
  2. L
  3. 2L/3
  4. 2L
  5. 4L

Question 2

If the speed of sound is 340 m/s, the length of the shortest open-closed pipe that resonates at 218 Hz is:

  1. 23 cm
  2. 17 cm
  3. 39 cm
  4. 78 cm
  5. 1.6 cm

Question 3

At 20^\circ {\rm C}, a pipe open at both ends resonates at a frequency of 440 Hz. At what frequency does the same pipe resonate on a particularly cold day when the speed of sound is 3 percent lower than …

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A collection of Doppler effect problems

Here is a set of four problems on the Doppler shift of sound waves. The solutions to the problems are given at the end. If you need a refresher on the Doppler effect, the following note might be useful: How does Doppler effect work?

Question 1

While standing at a crosswalk, you hear a frequency of 560 Hz from an approaching police car. After the police car passes and is moving away from you, you hear a frequency of 480 Hz. What is the speed of the police car (take speed of sound to be v=343 m/s)?

  1. 13.1 m/s
  2. 21.1 m/s
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Pulleys and masses connected to a spring

JEE Advanced 2019 Paper 2, Question 2

A block of mass 2 M is attached to a massless spring with spring-constant k. This block is connected to two other blocks of masses M and 2 M using two massless pulleys and strings. The accelerations of the blocks are a_{1}, a_{2} and a_{3} as shown in the figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is x_{0}. Which of the following option(s) is/are correct?

[g is the acceleration due to gravity. Neglect friction]

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  1. x_{0}=\frac{4 M g}{k}
  2. When spring achieves an extension of \frac{x_{0}}{2} for the first time, the speed of the
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How does Doppler effect work?

The Doppler effect for sound is a perceived difference between the frequency of sound heard by an observer and the actual frequency emitted by a source, due to relative motion between the source and the observer. A familiar example of this phenomenon is the change in sound frequency of an ambulance or fire engine as it rushes past you. We give a visual explanation of this effect and derive the relation between the observed and emitted frequencies below.

First, recall that the velocity of sound in a medium, v, is a property of the medium alone. That is, after the …

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Doppler effect and beats

JEE Advanced 2019 Paper 1, Question 15

A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When \mathrm{O} is 600 m away from S2 and distance between \mathrm{S} 1 and \mathrm{S} 2 is 800 m, what is the number of beats heard by O?

[Speed of the sound =330 m/s ]

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Recommended reading: How does Doppler effect work?


When there is relative motion between the source and observer, the observed frequency f_o is …

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