How Long Does Sound Travel Through Water and Copper?

[madd_bm]

Homework Statement

A sound wave is incident on a pool of fresh water. The sound enters the water perpendicularly and travels a distance of 0.52 m before striking a 0.18 m thick copper block lying on the bottom. The sound passes through the block, reflects from the bottom surface of the block, and returns to the top of the water along the same path. How much time elapses between when the sound enters and leaves the water

Homework Equations

for liquid:
speed = sqrt(Bulkmodulus / density) ...(this is the Adiabatic bulk modulus Bad

for solid:
v = sqrt (youngmodulus/density)

The Attempt at a Solution

liquid first:
sqrt (2.2e9/998.2071) = 1484.57 m/s ...this is the bulk modulus and density of water at ambient temperature (I had to assume it is at ambient temp, cause the equation does not say)

solid:
sqrt (1.1e11 / 8.94) ...young's modulus and density of copper

= 1.2416e10 m/s

then...

divide each distance by each individual speed. multiply each individual speed by 2 for round trip, then add the final numbers together to get:
7.04e-4

...but this is wrong. but you already know that...cause you're so friggin smart, you probably already know what I'm doing wrong.

thanks.

 

[alphysicist]

Hi madd_bm,

The Attempt at a Solution

liquid first:
sqrt (2.2e9/998.2071) = 1484.57 m/s ...this is the bulk modulus and density of water at ambient temperature (I had to assume it is at ambient temp, cause the equation does not say)

solid:
sqrt (1.1e11 / 8.94) ...young's modulus and density of copper

= 1.2416e10 m/s

I think you need to recalculate this speed; I believe you have made a calculation error.

 

[madd_bm]

Holy Cow. You're right. not sure where that number came from.
The actual answer I got (corrected calculations): 7.038e-4 unfortunately still wrong.

Thanks.