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 19 meters of a type of string has a mass of 31 grams, what is its linear mass density?

0.0163 kg/m0.589 kg/m5.89 kg/m0.00163 kg/m

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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 1.75 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).

0.0172 newtons0.549 newtons314 newtons56.0 newtons

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

5.80 m/sec18.3 m/sec0.0305 m/sec0.0183 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 41-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.

0.820 meters1.64 meters0.410 meters0.205 meters

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Question 5 At what frequency is the string resonating?

22.4 hz7.07 hz44.7 hz89.5 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 3.5 times that of the original string.

When 108 washers are added to this string and it is plucked, at what frequency will this second string resonate?

6.39 hz87.9 hz22.0 hz76.9 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.

0.403 hz8.06 hz10.98 hz11.18 hz