# An oscillator creates periodic waves on a stretched string

An oscillator creates periodic waves on a
stretchedstring.
*

If the period of the oscillator doubles,
whathappens to the wavelength and wave speed?
 The wavelength doubles but the wave speed isunchanged. The wavelength is halved but the wave speed isunchanged. The wavelength is unchanged but the wave speeddoubles.
*

If the amplitude of the oscillator
doubles,what happens to the wavelength and wave speed?
 The wavelength doubles but the wave speed isunchanged. The wavelength is unchanged but the wave speeddoubles. Both wavelength and wave speed areunchanged.

## General guidance

Concepts and reason

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.

Fundamentals

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.

## Step-by-step

### Step 1 of 2

(1)

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

…... (1)

Expression for the frequency of the wave is,

…… (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.

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.

### 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.