Reflection, standing waves in strings and organ pipes, harmonics — practice questions

Question 1 · difficulty L2 · understanding

A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be _________ cm.

Question 2 · difficulty L2 · understanding

An organ pipe $$40 \mathrm{~cm}$$ long is open at both ends. The speed of sound in air is $$360 \mathrm{~ms}^{-1}$$. The frequency of the second harmonic is ___________ $$\mathrm{Hz}$$.

Question 3 · difficulty L2 · understanding

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _________ degree.

Question 4 · difficulty L2 · understanding

A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is _________ Hz.

Question 5 · difficulty L2 · understanding

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by $$y = (10\cos \pi x\sin {{2\pi t} \over T})$$ cm The amplitude of the particle at $$x = {4 \over 3}$$ cm will be ___________ cm.

Question 6 · difficulty L2 · understanding

A wire having a linear mass density 9.0 $$\times$$ 10 $$-$$4 kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is ____________ m.

Question 7 · difficulty L2 · understanding

A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fork will be __________ cm. (Take speed of sound in air as 340 ms $$-$$1 )

Question 8 · difficulty L2 · understanding

Two travelling waves produces a standing wave represented by equation, y = 1.0 mm cos(1.57 cm $$-$$1 ) x sin(78.5 s $$-$$1 )t. The node closest to the origin in the region x > 0 will be at x = .............. cm.

Question 9 · difficulty L2 · understanding

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is $5 / x$. The value of $x$ is $\_\_\_\_$

• A. 3
• B. 2
• C. 4
• D. 1

Question 10 · difficulty L2 · understanding

In an open organ pipe $\nu_3$ and $\nu_6$ are $3^{\text {rd }}$ and $6^{\text {th }}$ harmonic frequencies, respectively. If $\nu_6-\nu_3=2200 \mathrm{~Hz}$ then length of the pipe is $\_\_\_\_$ mm . (Take velocity of sound in air is $330 \mathrm{~m} / \mathrm{s}$.)

• A. 200
• B. 225
• C. 275
• D. 250