# Physics

posted by .

A string is 37.5 cm long and has a mass per unit length of 5.95 10-4 kg/m. What tension must be applied to the string so that it vibrates at the fundamental frequency of 612 Hz?

The answer is supposed to be 125 N, but I'm not sure how to get this answer. So far, I have found the mass of the string to be 2.0235 x 10e-04 kg. I'm not sure if this is useful or not, though. Any guidance is greatly appreciated.

• Physics -

You need to know that the formula for the speed of travelling waves on a taut string is

V = sqrt(T/d).

where d is the lineal density per unit length, and T is the tension.

The fundamental frequency has a wavelength of twice the length, or 0.75 m. A standing wave at the fundamental frequency is two traveling waves going in opposite drections with wavelength 0.75 m and wave speed
V = (wavelength)*(frequency)
= (0.75 m)*612 Hz
= 459 m/s

Now you can use the wave speed equation to solve for the string tension, T

T = d*V^2 = 5.95*10^-4 * 459^2 = 125 N

## Similar Questions

1. ### Physics

The A string of a violin is 31 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length of 5.8×10^−4 kg/m. What are the wave speed in the string?
2. ### Physics

A 1.6-m-long string fixed at both ends vibrates at resonant frequencies of 792 Hz and 990 Hz, with no other resonant frequency between these values. (a) What is the fundamental frequency of this string?
3. ### physics

A 1.6-m-long string fixed at both ends vibrates at resonant frequencies of 792 Hz and 990 Hz, with no other resonant frequency between these values. (a) What is the fundamental frequency of this string?

A 60.00 cm guitar string under a tension of 46.000 N has a mass per unit length of 0.11000 g/ cm. (a) What is the speed of the wave?

A 60.00 cm guitar string under a tension of 46.000 N has a mass per unit length of 0.11000 g/ cm. (a) What is the speed of the wave?

A 60.00 cm guitar string under a tension of 46.000 N has a mass per unit length of 0.11000 g/ cm. (a) What is the speed of the wave?

A 60.00 cm guitar string under a tension of 46.000 N has a mass per unit length of 0.11000 g/ cm. (a) What is the speed of the wave?
8. ### Physics, waves

A string vibrates in its fundamental mode with a frequency of 200 Hz. The string is 0.64 m long and has a mass of 1.61 g. With what tension must the string be stretched?
9. ### Physics

A string of length L vibrates with a fundamental frequency f when under a tension of 100 N. What is the fundamental frequency of the string when its tension is increased to 2500 N?
10. ### physics

Where F is the tension in the string and µ is the linear density (mass per length) of the string. A violin string vibrates at the fundamental frequency of 512 Hz under the tension of 480 N. What should be the tension in the string …

More Similar Questions