# The speed of a wave traveling along a spring: a. depends on the amplitude of the wave. b....

## Question:

The speed of a wave traveling along a spring:

a. depends on the amplitude of the wave.

b. depends on the frequency of the wave.

c. depends on the tension in the spring.

d. depends on the mass of the spring.

e. More than one of the above.

f. None of the above.

## Mechanical Waves on a Spring

Spring is a coiled metallic wire designed to obey Hook's law over a definite range of force. In the simplest way, one can define spring as Hook's law of medium. Force is required to stretch the spring and the force required is proportional to the elongation in the spring. Springs are characterized by its spring constant, the force required to make unit stretching or compression in the spring.

- Transverse and longitudinal type of mechanical waves can travel through a spring.
- Frequency of a mechanical wave on a string can be expressed as {eq}F = \dfrac { v } { \lambda } {/eq}. Here {eq}v, \ \ \lambda {/eq} are the velocity of the wave on the spring and wavelength of the wave.

- Velocity of the mechanical waves on a spring depend on the mechanical properties of the spring.

## Answer and Explanation: 1

Transverse and longitudinal waves can exist in the spring.

Speed of a transverse wave on a spring of spring constant *k* stretched by a distance *x* can be expressed as {eq}v = \sqrt { \dfrac { k x } { \mu } }
{/eq}. Here {eq}\mu
{/eq} is the mass per unit length of the spring.

The linear mass density of a spring of length *L* and mass *m* can be expressed as {eq}\mu = \dfrac { m } { L }
{/eq}

The speed of the transverse wave on the spring {eq}v = \sqrt { \dfrac { k L x } { m } } {/eq}

Speed of longitudinal wave on the spring {eq}v = \sqrt { \dfrac { k L } { \mu } } \\ v = L \times \sqrt { \dfrac { k }{ m } } {/eq}

In terms of wavelength {eq}\lambda
{/eq} and frequency *F* speed of the wave {eq}v = F \times \lambda
{/eq}.

So we can conclude that the speed of the wave on a spring depends on the (i) tension on the spring, ( ii) mass of the spring, ( iii) length of the spring, ( iv) Frequency, and ( v) Wavelength.

We can see that many of the options on which the speed of the wave depends.

Therefore the correct option is **option e )**

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Chapter 4 / Lesson 19After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.