VIBRATING STRING

Name:_____________________________    Course:_______________ Time:___________

Partners:___________________________________________________________________________

Purpose: To investigate sound waves in a stretched string and determine the speed of sound in the string.

Apparatus: String vibrator, string, mass set, mass hanger, electronic balance, meter stick, and pulley w/clamp.

Theory: Stringed musical instruments are played by plucking or bowing a stretched string. In this investigation a string vibrator will make the string to vibrate at a frequency of 120 Hz. The tension will be provided by a hanging mass. The vibrations will travel along the string and get reflected at the other end. The reflected waves and the incoming waves will interfere and form standing waves. By varying the tension (T) standing waves with different number of loops can be obtained. The standing waves for two and three loops are shown below. One loop length is half the wavelength.

In terms of hanging mass, m and acceleration due to gravity, g tension, T is given by:  T = mg.

In terms of frequency, f and wavelength, 8 the wave speed, V is given by:   V = 8f.

In terms of tension, T and mass per length, µ the wave speed, V is given by:  V = sq.root(T/µ) 

µ = Mass/Length: Mass per length, µ is a property of the string which tells us whether the string is "heavy" or "light". You may know that the four violin strings are not the same. Some are thick and others are thin. The heavy strings are used for low tones and the light ones are for high tones. In this investigation you will determine µ, by measuring the length and mass of thestringbefore attaching it to the vibrator.

DATA: USE SI UNITS.

Length of string = ________________ Mass of string = _________________

Mass/length = µ = ________________

Frequency = f = 120 Hz,   Acceleration due to gravity = g = 9.8 m/s²

Conclusion:

Questions:                                                                       

        1. The amplitude of the wave in the figure is________________

        2. The period is______________________

        3. The frequency of the wave is__________________

A stretched string, fixed at both ends, vibrates at a frequency of 12 Hz with a standing transverse wave pattern as shown.

4. What is the fundamental frequency?__________

5. What would be the frequency of the first overtone?____________

6. If the string is 5 meters long, what is the wave velocity?__________

7. If a string has a wave speed of 200 m/s and a mass per length ratio of 1.2 g/m, what is the tension?

8. A stretched cord has a fundamental frequency of 144 Hz, a length of .9 m, and a mass of 2 g. What is its wave speed?

9. A stretched cord has a fundamental frequency of 144 Hz, a length of .9 m, and a mass of 2 g. What is the tension on the cord?