# MCQs: Standing waves

Standing waves

1. 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

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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 = πr2l x ρ
same material and length so f ∝ 1/r
So if r is doubled f is halved

2. The diagram below represents the frequency spectrum of a musical instrument.

A.  Violin
B.  Guitar
C.  Flute
D.  Clarinet

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3.
4.

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.

3. 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

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3.
4.

v = √(Tension/mass per unit length)

4. 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

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To get the same wavelength the pipe would have to be at least twice as long

5. 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

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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.

6. 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

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Length = 2 x wavelength

7. 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.

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3.
4.

Only the first one has points where the amplitude is zero.

8. 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.

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You don't get a standing wave if the frequencies are different.

9. 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?

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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.

10. 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.

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At point P the waves sometimes produce a peak sometimes a trough and sometimes nothing so its an antinode.

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