6. Investigating Resonance

Question 1

What factors can affect the resonant frequencies?

Answer 1

1. Mass
2. Length
3. Tension

Question 2

Describe the method of investigating resonant frequency

Answer 2

1. Measure mass and length of strings of different types using mass balance and ruler to find the mass per unit length
2. Record μ
3. Measure and record length, l, between vibration transducer and the pulley
4. Work out tension on the string
5. Turn on signal generator and vary frequency at which vibration transducer vibrates
6. Find the first harmonic
7. The frequency of the signal generator shows the frequency of the first harmonic, f
8. Move vibration transducer towards or away from pulley to change length of vibrating string
9. Add masses to change tension on string
10. Use range of string samples of varying masses to change μ

Question 3

What is the equation for mass per unit length?

Answer 3

μ = M / L

μ = mass per unit length (kg/m)
M = mass of string (kg)
L = length of string (m)

Question 4

How do you work out the tension in the string?

Answer 4

T = mg

T = tension on string (N)
m = total mass of masses added to string (kg)
g = acceleration due to gravity (ms^-2)

Question 5

What is the relationship between length and resonant frequency?

Answer 5

The longer the string, the lower the resonant frequency (if λ increases, f decreases for fixed c)

Question 6

What is the relationship between mass per unit length and resonant frequency?

Answer 6

The heavier the string, the lower the resonant frequency (waves travel more slowly down the string because for a given length, a lower velocity, c, makes a lower frequency, f)

Question 7

What is the relationship between tension and resonant frequency?

Answer 7

The lower the tension on the string, the lower the resonant frequency (waves travel more slowly down a loose string)

Question 8

What is the equation for calculating resonant frequency?

Answer 8

f = 1/2l √(T/μ)

f = frequency (Hz)
l = length of vibrating string (m)
T = tension on string (N)
μ = mass per unit length (kg/m)