PhysicsLAB Practice Problems
Vibrating Strings

Directions: On this worksheet you will be investigating the interference properties along a vibrating string and its wave velocity.

Question 1  If 21 meters of a type of string has a mass of 32.5 grams, what is its linear mass density?
Question 2  A section of this string is secured on one side of a sounding board and 32 washers are hung from its other end.

If each washer has a mass of 1.50 grams, what is the tension along the string? Recall that the tension is produced by the weight of the suspended washers: weight (measured in newtons) = mass (measured in kilograms) times gravity (9.8 m/sec2).
Question 3  What will be the speed of any wave that travels along this string?
Question 4  The center of the string is now lightly plucked setting the string into vibration. If only one loop is produced along the 42.5-cm long vibrating segment, what is the wavelength of the string's frequency?

Recall that a loop (N-A-N) represents one-half of a wavelength.
Question 5  At what frequency is the string resonating?
Question 6  A second string, having the same length, is now added to the sounding board. It has a linear mass density that is 3 times that of the original string.

When 92 washers are added to this string and it is plucked, at what frequency will this second string resonate?
Question 7  How many beats would be heard between the two strings over a period of 20 seconds? Recall that one beat is heard each second when the difference in the frequencies between two sources is one hertz.

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