12. Another investigation of waves using a tensioned wire and signal generator

A The set-up

This method involves using a signal generator is connected to a vibration transducer.

A longish piece of wire or string is fixed to the vibration transducer and passed over a pulley wheel at the end of the bench.

The other end of the wire/string is connected to a hook system on which you can add 'weights' to increase the tension on the wire/string.

 

B The procedure

You switch on the signal generator and vibration transducer to set the wire/string vibrating - the waves should oscillate up and down.

Adjust the frequency until you can get a clear transverse standing wave (as in diagram B) and measure its wavelength using the metre rule sighted behind the vibrating wire/string.

Its easiest to measure the length of as many half wavelengths as you can, calculate the average and then double the average to get the full wavelength.

You can vary two things:

(i) Vary the weights added to tension the string and measure the wavelength each time for a fixed length of wire/string between the transducer and the pulley wheel.

(ii) Vary the length of the wire/string between the transducer and the pulley wheel for a fixed tension weight.

Obviously, you can do several sets of results within the experimental framework of (i) and (ii).

 

Measurements and calculations

For each set of experiments you should record

the frequency of the standing wave (f in Hz)

the tension on the string/wire (T in N)

the total length of the wire/string (L in m)

the wavelength (λ in m)

and you can calculate the speed too (v = f x λ in m/s).

This gives you loads of data to play with!

You should find that the wavelength of the string wire measured varies with:

(i) The in tension on the wire/string for a fixed length.

You should find the frequency increases and wavelength decreases the greater the tension on the wire/string.

The frequency is proportional to the square root of the tension (f 1/√T).

Think of tightening the tension on a guitar or violin string (fixed length) - the pitch increases the more you tighten it up.

(ii) The length of the wire/string for a fixed tension weight.

You should find that the frequency increases and wavelength decreases the shorter the wire/string.

For a fixed tension weight, the frequency of a stretched string is inversely proportional to the length of the string (f 1/L).

 

Having measured the wavelength (convert to m), and knowing the frequency (Hz) from the generator, you can then calculate the speed of the wave in each case.

speed = frequency x wavelength = v = f x λ = ? m/s

For more see measuring the speed of sound in air