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Q. 2

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 450

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Short Answer

A wave pulse travels along a stretched string at a speed of 200 cm/s. What will be the speed if:

a. The string’s tension is doubled?

b. The string’s mass is quadrupled (but its length is unchanged)?

c. The string’s length is quadrupled (but its mass is unchanged)?

Note: Each part is independent and refers to changes made to the original string

a) The speed of the wave is 282.2 cm/s when the string's tension is doubled.

b) The speed of the wave is 100 cm/s when the string’s mass is quadrupled.

c) The speed of the wave is 400 cm/s when the string’s length is quadrupled.

See the step by step solution

Step by Step Solution

Step 1. Write the given information.

The velocity of the wave is v = 200 cm/sLet the tension of the string is T.The mass of the string is m.

The length of the string is L.Let the effective mass is denoted by

Step 2. a) To determine the velocity of the wave when tension is doubled.

The speed of the wave in the string is given by

The speed is directly proportional to the tension, and length of the string and inversely proportional to the mass of the string.When the tension is doubled, the new speed of the wave is given by,

The speed of the wave increases as the tension is doubled. The new speed is 282.2 cm/s

Step 3. b) To determine the velocity of the string’s mass is quadrupled.

When the mass of the string is quadrupled, the new speed isThe new speed of the wave is 100 cm/s

Step 4. c) To determine the velocity of the string’s length is quadrupled.

When the length of the string is quadrupled, the new speed of the wave is

The new speed of the wave is 400 cm/s.

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