The wavelength doubles but the wave speedisunchanged.

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The wavelength is halved but the wave speedisunchanged.
The wavelength is unchanged but the wavespeeddoubles.

Both wavelength and wave speedareunchanged.
The wavelength is unchanged but the wavespeeddoubles.
The wavelength doubles but the wave speedisunchanged.

The concepts used to solve this problem are wavelength of the wave and wave speed in string.

Wavelength of the wave is the distance between two successive points on a wave that are in the same state of oscillation.

Use the expression of wavelength of wave in terms of speed and frequency of the wave to find the dependence of period on wavelength of the wave.

Wave speed is the speed in which wave can travel.

Use the expression of wave speed on a string to find the dependence of period on wave speed.


The expression of wavelength of wave in terms of speed and frequency of the wave is,

*

Here,

*
is the frequency of the wave,
*
is the wavelength of the wave, and
*
is the speed.

Expression for the frequency of the wave is,

*

Here,

*
is the period of the wave.

Expression for the wave speed in string is,

*

Here,

*
is the wave speed in string,
*
is string tension,
*
is string mass, and
*
is string length.


(1)

The expression of wavelength of wave in terms of speed and frequency of the wave is,

*
\u2026... (1)

Expression for the frequency of the wave is,

*
\u2026\u2026 (2)

Substitute

*
for
*
in equation (1).

*

If the period of the oscillator doubled then,

Substitute

*
for
*
.

*

Hence, if the period of the oscillator doubles the wavelength also doubles.

Expression for the wave speed in string is,

*

Here, t is the tension in the string.

The speed of the wave does not depend on the period of the wave. Hence, the wave speed remains unchanged when the period of the oscillator doubles.

Therefore, the correct option is the wavelength doubles but the wave speed is unchanged if the period of the oscillator doubles.


Part 1

The wavelength doubles but the wave speed is unchanged.


Explanation | Common mistakes | Hint for next step

The wavelength of the wave is directly proportional to the period of the wave and speed.

The increase in the period will increase the wavelength of the wave.

The wave speed in string is directly proportional to the square root of the tension in the string and inversely proportional to the square root of linear mass density.

The period is independent of the wave speed in string. Hence the increase in the period does not affect the wave speed in string.


The incorrect expression for the wavelength of wave in terms of speed and frequency of the wave is

*
because the correct expression for the wavelength of wave in terms of speed and frequency of the wave is
*
.


Use the expression of wavelength of wave and the wave speed in string to find the dependence of the amplitude of the oscillator on the wavelength and wave speed when the amplitude of the oscillator doubles.


Step 2 of 2


(2)

The expression of wavelength of wave in terms of speed and frequency of the wave is,

*

Expression for the wave speed in string is,

*

Here, t is the tension in the string.

The wavelength and speed of the wave do not depend on the amplitude of the oscillator. Therefore, both the wavelength and wave speed are unchanged if the amplitude of the oscillator doubles


Part 2

Both the wavelength and wave speed are unchanged.


When waves travel along a string the wave speed remains unchanged, unless the properties of the string are changed.

The wavelength can be varied only by changing the period of the oscillator that create the waves.

Amplitude have no effect on wave speed and wavelength. Hence the wavelength and wave speed are unchanged if the amplitude of the oscillator doubles.


The incorrect expression for the wave speed in string is

*
because the correct expression for the wave speed in string is
*
.


Answer


Part 1

The wavelength doubles but the wave speed is unchanged.


Part 2

Both the wavelength and wave speed are unchanged.


Answer only


Part 1

The wavelength doubles but the wave speed is unchanged.


Part 2

Both the wavelength and wave speed are unchanged.


10
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Answer #1

Part A

If the period of the oscillator doubles, what happens to thewavelength and wave speed?

The wavelength doubles but the wave speed is unchanged.

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Correct

Part B

If the amplitude of the oscillator doubles, what happens to thewavelength and wave speed?

Both wavelength and wave speed are unchanged.

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Correct

As you have discovered, when waves travel along a string, thewave speed remains unchanged, unless the properties of the stringare changed. The wavelength can be varied only by changing thefrequency, or alternatively the period, of the oscillator thatcreates the waves.


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