Urgent!! Suppose you set off a standing wave on a string with 2 segments. The fr

Question

Urgent!! Suppose you set off a standing wave on a string with 2 segments. The frequency of the driving source is 60 Hz . The string has a linear density of 8.15×104 kg/m and a length of 0.96 m (between where it is tied to the vibrator to where it passes over the pulley). You find that in order to get your neat, 2-segment standing wave, you have to hang a mass of 290 g .

a)

What is the tension in the string?

Enter your answer in Newtons, with 3 significant figures.

b)

What is the speed of the wave based on the tension?

Enter your answer in meters per second, with 3 significant figures.

c)

What is the wavelength of this standing wave?

Enter your answer in meters, with 3 significant figures.

d)

What is the speed of the wave based on the frequency and wavelength of the wave?

Enter your answer in meters per second, with 3 significatn figures.

e)

Calculate the percent difference between the values you found for the velocity of the wave based on the tension and based on the frequency. Use the velocity based on the frequency as the "accepted" value and take the absolute value of your result.

Enter a positive percent value.

Explanation / Answer

Given that

The frequency of the driving source is(f) = 60 Hz .

The string has a linear density of (u) =8.15×104 kg/m

The length of the string(L) = 0.96 m

Mass hanged is (m) =290g =290*10-3kg =0.29kg

a)

We know that velocity of the wave is given by

v =Sqrt(T/(m/L)

We also know that

v =f*lamda

Given that two segments means it is equal to lamda =L

v =f*L

f =v/L =v =Sqrt(T/(m/L)/L

=(1/L)*Sqrt(T/(m/L)

The tension in the string is given by T =f2*L2*(m/L) =(60)2*(8.15×104 kg/m )*(0.96)2 =2.703N

b)

The speed of the wave is given by

v =Sqrt(T/m/L) =Sqrt(2.816/(8.15×104 kg/m )) =58.7810m/s

c)

The wavelength of the standing wave lamda =L =0.96m

d)

The speed of the wave based on frequency and wavelength is

v =f*lamda = 60*0.96 =57.6m/s

e)

Calculate the percent difference between the values you found for the velocity of the wave based on the tension and based on the frequency.

( 57.6 - 58.781/57.6)*100 =2.05%

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