A standing wave pattern is created on a string with mass density = 3.4 × 10 -4 k

Question

A standing wave pattern is created on a string with mass density = 3.4 × 10-4 kg/m. A wave generator with frequency f = 61 Hz is attached to one end of the string and the other end goes over a pulley and is connected to a mass (ignore the weight of the string between the pulley and mass). The distance between the generator and pulley is L = 0.61 m. Initially the 3rd harmonic wave pattern is formed.

1)

What is the wavelength of the wave?

m

2)

What is the speed of the wave?

m/s

3)

What is the tension in the string?

N

4)

What is the mass hanging on the end of the string?

kg

5)

Now the hanging mass is adjusted to create the 2nd harmonic. The frequency is held fixed at f = 61 Hz.

What is the wavelength of the wave?

m

6)

What is the speed of the wave?

m/s

7)

What is the tension in the string?

N

8)

What is the mass hanging on the end of the string?

kg

9)

Keeping the frequency fixed at f = 61 Hz, what is the maximum mass that can be used to still create a coherent standing wave pattern?

kg

Explanation / Answer

speed , v = 2Lf/n = 2*0.61 * 61/(3) = 24.80 m/s

1) L = 24.80/61 = 0.406 m

2) v = 24.80 m/s

3) T = mu*v^2 = 3.4*10^-4*(24.80^2) = 0.209 N

4) mass m = 0.209/9.8 = 0.0213 kg = 21.3 g

6)

v = 2Lf/n , where n =2

v = 2*0.61*61/2 = 37.21 m/s

5) L = 37.21/61 = 0.61 m

7) T = mu* v^2 = 3.4*10^-4 *37.21^2 = 0.4707 N

8) m = T/g = 0.4707/9.8 = 0.048 kg

9) for fundamental frequency m = 0.012 kg

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