1.The tension in the string is generally provided by weights on a hanger, but wh

Question

1.The tension in the string is generally provided by weights on a hanger, but while experimenting with the system you can use your hand to apply extra force. With the frequency fixed (in a third harmonic system), consider pressing down on the hanger (effectively adding extra weight to the hanger) until you reach a different resonance. What would happen to each of the following quantities? State whether it increases, stays the same or decreases and why. a) Tension in the string b) Velocity of waves traveling back and forth along the string c) Number of antinodes d) Wavelength of the standing wave on the string. 2. The goal of the third experiment is to measure the velocity of sound in air using standing waves in a tube. What factors (velocity of a wave, frequency, length of tube, wavelength of standing wave) are kept constant in the experiment and which factor is varied?

Explanation / Answer

We know that

The velocity of the wave along the string is given by

v =Sqrt(T/u)     where u =m/L   mass per unit length

a)

Adding extra weight increases the force, therefore the tension also increases.

b)

If tenison increases, then velocity and tension are directly proportional to each other then velocity also increases.

c)

There will be three antinodes in the 3rd harmonic that remains constant.

d)

The speed of the wave is

v =Sqrt(T/u)

for the 3rd harmoninc f3 =3v/2/L

f*lamda =Sqrt(T/u)

Now the frequency remains constant, therefore the wavelngth increases then the tension also increases

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