If a wind instrument, such as a tuba, has a fundamental frequency of 56.0 Hz, what are its first three overtones (in Hz)? It is closed at one end. (The overtones of a real tuba are more complex than this example, because it is a tapered tube.)

168 Hz, 280 Hz and 392 Hz

Explanation:

The resonant frequencies for a closed pipe at one end is given by :

, n = 1,3,5...

The fundamental frequency, f₁ = v/4l = 56 Hz

For first overtone, put n = 3

For second overtone, put n = 5

For third overtone, put n = 7

So, the first three overtones are 168 Hz, 280 Hz and 392 Hz.

98.4 m

explanation:

let s = distance up the plane  

then by conservation of energy  

1/2m(18.3)^2 = mg s sin(10)  

(18.3)^2 = 2g s sin(10)  

s = (18.3)^2/2gsin(10)  

= 98.39564526  

= 98.4 m