Athin string 2.50 m in length is stretched with a tension of 90.0 n between two supports. when the string vibrates in its first overtone, a point at an antinode of the standing wave on the string has an amplitude of 3.50 cm and a maximum transverse speed of 28.0 m/s. (a) what is the string’s mass? (b) what is the magnitude of the maximum transverse acceleration of this point on the string?

The string's mass and the maximum transverse acceleration are 2.2 g and 22400.51 m/s².

Explanation:

Given that,

Length of string = 2.50 m

Tension = 90.0 N

Amplitude = 3.50 cm

Speed = 28.0

First overtone ,

(a). We need to calculate the mass of string

Using maximum transverse speed at antinodes

Put the value into the formula

Using formula of wavelength

Mass of string =

Mass of string =

Mass of string =2.2 g

(b). We need to calculate the maximum transverse acceleration of this point on the string

Using formula of the maximum transverse acceleration

Put the value into the formula

Hence, The string's mass and the maximum transverse acceleration are 2.2 g and 22400.51 m/s².

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