A particular guitar string has a mass of 3.0 grams and a length of 0.75 m. A standing wave on the string has the shape shown in the simulation above - the wave has a frequency of 1200 Hz.

(a) What is the speed of the wave?

(b) What is the tension of the string?

(c) What is the fundamental frequency of the string?

(d) The wave on the string produces a sound wave. Does the sound wave have the same frequency, wavelength, and/or speed as the wave on the string?

Part (a). The speed of the wave is given by:

v = fλ

From the simulation, it can be seen that he wavelength is 2/3 of the length of the string (1.5λ = L).

λ = 0.50 m and f = 1200 Hz, so:

v = 1200 * 0.5 = 600 m/s.

Part (b). The tension in the string can be found from the relationship:

v

=

(

T μ

)

½

where μ, the mass per unit length of the string, is

μ

=

0.003 0.75

= 0.004 kg/m

T = μ v² = 0.004 *600*600 = 1440 N

Part (c). As shown the string vibrates at a frequency of 1200 Hz. What is the fundamental frequency of the string?

1. 300 Hz (1/101) (1%)
2. 400 Hz (65/101) (64%)
3. 600 Hz (4/101) (4%)
4. 800 Hz (16/101) (16%)
5. 1200 Hz (12/101) (12%)
6. 1800 Hz (3/101) (3%)
7. 2400 Hz (0/101) (0%)
8. 3600 Hz (0/101) (0%)
9. 4800 Hz (0/101) (0%)

Part (d). The vibrating string produces a sound wave. What is the same for the wave on the string and the sound wave?

1. the frequency (74/102) (72%)
2. the speed (2/102) (2%)
3. the wavelength (2/102) (2%)
4. all of the above (21/102) (21%)
5. none of the above (3/102) (3%)

The frequency. The speed is set by properties of the medium. The two waves travel through completely different media (string and air) so the speeds are different. The particles in the air vibrate back and forth at the frequency of the wave on the string, so the frequency must be the same.