A long string is composed of two different materials. The leftside has a smaller

Question

A long string is composed of two different materials. The leftside has a smaller linear mass density than the right side. Thecomposite string is placed under a uniform tension, then the leftside is vibrated with a constant frequency. It is observed that thewavelength on the light string is twice that of the heavystring. 1. what is the ratio of the linear mass densities? 2. what is the ratio of the amplitudes of vibration? 3. what is the ratio of the transverse speeds? 4. what is the ratio of the propagation speeds? 5. what is the fraction of incident energy that is transmittedto the more massive string? I promise to rate you as lifesavers if youranswer is correct! A long string is composed of two different materials. The leftside has a smaller linear mass density than the right side. Thecomposite string is placed under a uniform tension, then the leftside is vibrated with a constant frequency. It is observed that thewavelength on the light string is twice that of the heavystring. 1. what is the ratio of the linear mass densities? 2. what is the ratio of the amplitudes of vibration? 3. what is the ratio of the transverse speeds? 4. what is the ratio of the propagation speeds? 5. what is the fraction of incident energy that is transmittedto the more massive string? I promise to rate you as lifesavers if youranswer is correct! I promise to rate you as lifesavers if youranswer is correct!

Explanation / Answer

given left side have constant linear mass density =m1 right side linear mass density = m2 tenstion is constant rightside string has smaller linear mass density so itis lighther string wave length on the light string is1= heavy string wave length = 2 =21 we know that , n = 1/2l T/m from above eq n1= 1/2lT/m1 for left string for right string = n2= 1/2lT/m2 but n1 = v/1 and n2= v/2 plug n1and n2 values in the aboveeq then 2/1=m2/m1     2=m2/m1 squring on both sides 4 = m2/m1 m2= 4m1 tranverse speeds v1 = T/m1                          v2= T/m2 then v1/v2 =m2/m1                   =2 I hope this will help you.                   =2 I hope this will help you.   

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