You are making a telephone out of two aluminum cans and some string. you can choose between two types of string: a 2-m length of thin cooking twine or a 2-m length of heavy rope. which type of string should you use so that you have the fastest wave speed in your telephone?

This problem can be better understood by looking at how a sound wave propagates through a string.

The speed of a sound wave through a string or a rope is given by the formula,

, where is the tension on the string and is the density of the string. From the formula, we can read that the speed of sound is fastest in ropes with big tension and very low density. Assuming that both the twine and the rope would be kept at the same tension, the twine has the lowest density of the two.

To get the fastest wave of sound for this model, the thin cooking twine has to be used.

The 2 m long thin cooking twine wire will be much more appropriate to design the telephone out of two aluminum cans.

Further Explanation:

The telephone made out of the aluminum cans make use of the transmission of the sound wave from one end of the can through the wire and it is heard by the user at the other end of the wire.

The transmission of the sound wave depends on the medium through which it is passed. The velocity of the sound wave through the medium is the key property which is of primary importance for the transmission of the sound wave from one end to the other end.

The velocity of the sound wave is expressed as:

Here,  is the velocity of the sound wave,  is the young’s modulus and  is the density of the medium through which the sound is transmitted.

Since the density of the twine wire is less as compared to that of the rope, the sound wave will have higher velocity when they are transmitted through the twine wire as compared to the rope of same length.

Thus, the 2 m long thin cooking twine wire will be much more appropriate to design the telephone out of two aluminum cans.

Learn More:

1. A sound wave is described by d(y,t)=(0.0200mm)× sin[(8.96rad/m)y+(3140rad/s)t+pi/4rad],

2. You see condensed steam expelled from a ship’s whistle 2 s before you hear the sound

3. An astronaut takes her bathroom scales to the moon, where g = 1.6 m/s2

Answer Details:

Grade: High School

Subject: Physics

Chapter: Sound Waves

Keywords:

Telephone, aluminum cans, two types of strings, thin cooking twine, heavy rope, fastest wave speed, much more appropriate, density of twine, sound wave, transmitted.