Question

You are given a long length of string and an oscillator that can shake one end of the string at any desired frequency. The oscillator has a display that indicates the frequency. You are asked to design an experiment to study how the velocity of waves on the string depends on the string's tension. You do not have any way to measure time with sufficient accuracy to help in your investigation.

A. Describe your experimental setup and procedure, including any additional pieces of equipment you would need and the kind of data you would record. Include enough detail that another student could follow and complete the experiment successfully.



B. Describe how you would analyze your data to obtain information about the wave velocity's dependence on tension.

Answer 1

Step-by-step explanation:

a.

AIM :

TO STUDY HOW VELOCITY OF WAVES ON THE STRING DEPENDS ON THE STRING'S TENSION.

APPARATUS:

Oscillator, long strings , some masses( to create tension in string) and the support ( rectangular wooden piece).

EXPERIMENTAL SETUP:

1. Measure the length of the string and mass of the weights used.

2. Connect one end of string to the oscillator.

3. Place the support below string on table such that the string is in same line without touching table.

4. After the support, the string should hang freely.

5. The other end of string is connected with some small measured masses which should be hanging.

PROCEDURE:

1. Note down the length of string and mass of weights.

2. Adjust the frequency in the oscillator which creates standing waves in the string.

3. Start from lower frequency and note down the lowest frequency at which mild sound is heard or when string forms one loop while oscillating.

4. Calculate the wavelength using of waves using length of string.

5. Calculate the velocity using frequency and wavelength.

6. Calculate linear mass density.

8. Repeat the procedure with different masses.

7. plot a graph with tension in y axis and linear mass density in x axis.

8. Find slope and compare with velocity.

Linear mass density

µ = m/l(kg-1)

tension

T = m x 9.8N

wave length

ƛ = 2L

b.

We can analyze the data by comparing slope of the graph, tension Vs linear mass density with velocity which is constant for constant length.

Write the slope value in terms of value of velocity and find the relationship between velocity and string's tension.

The expected result is

slope = v²

T ∝ V²