Oscillations and Waves

A collection of problems on standing waves

April 24th, 2022jeefirst0 Comments

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:

$L/2$
$L$
$2L/3$
$2L$
$4L$

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:

23 cm
17 cm
39 cm
78 cm
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 …

A collection of Doppler effect problems

April 9th, 2022jeefirst0 Comments

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)?

13.1 m/s
21.1 m/s

…

Pulleys and masses connected to a spring

January 14th, 2022jeefirst0 Comments

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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$x_{0}=\frac{4 M g}{k}$
When spring achieves an extension of $\frac{x_{0}}{2}$ for the first time, the speed of the

…

How does Doppler effect work?

January 7th, 2022jeefirst0 Comments

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 …

Doppler effect and beats

January 6th, 2022jeefirst0 Comments

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?