Question

The speed of longitudinal waves traveling in a long, solid rod is given by the following equation, where Y is Young's modulus and ? is the density of the solid.

v = sqrt((Y )/(?))

If a disturbance has a frequency of 44 Hz, what is the wavelength of the waves it produces in each of the following substances? [Hint: See Tables 9.1 and 9.2.]

(a) an aluminum rod m

(b) a copper rod m

Answer 1

v = sqrt(Y/?)
v = f?

here you have not provided the hint table about Y and ? values for aluminum and copper rods.

So, I have taken as Y_al = 7x10¹⁰ N/m² , ?_al = 2.7x10³ kg/m³

And Y_Co =11x10¹⁰N/m², ?_Co = 8.9x10³ kg/m³

1. 
   v = sqrt(Y/?)
   f? = sqrt(Y/?)
   ? = sqrt(Y/?) / f
   = sqrt[(7.0x10¹⁰ N/m²) / (2.7x10³ kg/m³)] / (44 Hz)
   ? = sqrt (2700)/44

? =51.96/44

? = 1.181m


b)
? = sqrt(Y/?) / f
= sqrt[(11x10¹⁰ N/m²) / (8.9x10³ kg/m³)] / (44 Hz)
= sqrt (8900)/44

= 94.34 /44

? =2.144m