Vibrating Strings

Practice Problems
Vibrating Strings

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

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Question 1 If 22 meters of a type of string has a mass of 37.55 grams, what is its linear mass density?

0.0171 kg/m0.826 kg/m0.00171 kg/m8.26 kg/m

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Question 2 A section of this string is secured on one side of a sounding board and 35 washers are hung from its other end.

If each washer has a mass of 1.00 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).

343 newtons0.0098 newtons35.0 newtons0.343 newtons

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Question 3 What will be the speed of any wave that travels along this string?

4.48 m/sec0.0204 m/sec14.2 m/sec0.0142 m/sec

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Question 4 The center of the string is now lightly plucked setting the string into vibration. If only one loop is produced along the 47.55-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.

0.476 meters0.951 meters0.238 meters1.90 meters

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Question 5 At what frequency is the string resonating?

4.71 hz59.6 hz14.9 hz29.8 hz

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Question 6 A second string, having the same length, is now added to the sounding board. It has a linear mass density that is 2 times that of the original string.

When 66 washers are added to this string and it is plucked, at what frequency will this second string resonate?

57.9 hz14.5 hz28.9 hz7.45 hz

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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.

8.64 hz7.45 hz0.432 hz7.24 hz