# MCQs: Standing waves

**Standing waves**

- Two strings X and Y have the same tension and length and are made of the same material but the diameter of Y is twice that of X. I frequency of X is 200 Hz the frequeny of Y is
A. 100 Hz

B. 150 Hz

C. 50 Hz

D. 33 Hz*f = 1/2l√T/μ so f ∝1/√μ**μ = mass/length length is the same for each so f ∝ 1/√m*

m = Volume x density = πr^{2}l x ρ

same material and length so f ∝ 1/r

So if r is doubled f is halved - The diagram below represents the frequency spectrum of a musical instrument.
A. Violin

B. Guitar

C. Flute

D. Clarinet*Hah got you.*

Bet you didn't know the clarinet was a closed pipe, its not the far end thats closed but the one you blow into.

Well, I didn't know anyway.

If your not sure why it has to be a closed pipe its because the closed pipe only has odd harmonics. - Which of the following makes the velocity of a wave in a stretched string greater?
A. Tightening

B. Plucking harder.

C. Using a thicker string.

D. Shortening the string*v = √(Tension/mass per unit length)* - The 1st harmonic of a closed pipe of length L is 300 Hz. To play the same note on an open pipe the length of the pipe could be
A. ¼L

B. ½L

C. L

D. 2L*To get the same wavelength the pipe would have to be at least twice as long* - A stretched string is plucked and a note of 150 Hz is produced. The frequency of the third harmonic is
A. 50 Hz

B. 100 Hz

C. 300 Hz

D. 450 Hz*A very boring question but when done produces a very nice sound.*

Here is Steve Hacket of Genesis putting some harmonics to good use, take a break and listen to this classic. The Harmonics come at the end. - The animation shows a standing wave in a stretched string.
If the wavelength of the wave is 10 cm the length of the string is

A. 5 cm

B. 20 cm

C. 10 cm

D. 15 cm*Length = 2 x wavelength* - The following animations represent waves
Which ones are standing waves?

A. Just the first.

B. The second and third.

C. All of them.

D. None of them.*Only the first one has points where the amplitude is zero.* - A sound wave of frequency 100 Hz meets with one of frequency 150 Hz travelling in the opposite direction. The result is
A. a standing wave of frequency 125 Hz.

B. a standing wave of frequency 250 Hz.

C. complete cancellations of the sound wave.

D. no standing wave.*You don't get a standing wave if the frequencies are different.* - The picture below represents two waves of frequency 1Hz travelling towards each other.
Which of the following diagrams represents the position of the waves after 1s?

*The wavelength of the waves are 2cm so their speed is 1 x 2 = 2ms*^{-1}In 1s each wave will therefore progress 2cm (one whole wavelength) the length of the black line between the waves.

- The picture shows two identical waves travelling towards each other. When the meet they will add to form a standing wave. The point marked with a P will be
A. a node

B. an antinode

C. neither node or antionode

D. midway between a node and antinode.*At point P the waves sometimes produce a peak sometimes a trough and sometimes nothing so its an antinode.*