Fundamental frequency / sound waves

[jsalapide]

1.Calculate the fundamental frequency of a steel rod of length 2.00 m. What is the next possible standing wave frequency of this rod? Where should the rod be clamped to excite a standing wave of this frequency?

first, i used the formula velocity of sound in the rod v=sqrt(Y/p)
where Y=20x10^10 Pa and p=7800 kg/m^3
i got 5063.7 m/s

then i substitute it to the formula for frequency f=v/4L
where L is the length of the rod..
my answer was 632.96 Hz

is that correct?

i cannot answer the succeeding questions.. please help..

 

[AvroArrow]

Yes, that is correct. The next possible standing wave frequency of the rod would be 1265.9 Hz. To excite a standing wave of this frequency, the rod should be clamped at one end and a node (point of no displacement) should be located at 1.00 m along the rod from the clamp.

 

[nlightner]

I can confirm that your calculation for the fundamental frequency of the steel rod is correct. However, I would like to point out that the velocity of sound in a material also depends on its density and elasticity, so it is important to use the correct values for these parameters in your calculation.

To determine the next possible standing wave frequency of the rod, we need to consider the different modes of vibration that can occur in the rod. The fundamental frequency corresponds to the first mode of vibration, where the rod vibrates as a whole. The next possible standing wave frequency would correspond to the second mode of vibration, where there is a node (point of no vibration) in the middle of the rod and two antinodes (points of maximum vibration) at the ends.

To calculate this frequency, we can use the formula f=3v/4L, where v is the velocity of sound in the rod and L is the length of the rod. Substituting the values we calculated earlier, we get a frequency of 949.44 Hz for the second mode of vibration.

To excite a standing wave of this frequency, the rod should be clamped at the middle point, as this is where the node will be located. This will allow the rod to vibrate in its second mode, producing a standing wave with a frequency of 949.44 Hz.

It is important to note that there are many other possible standing wave frequencies for this rod, corresponding to different modes of vibration. These can be calculated using the formula f=nv/4L, where n is the mode number. For example, the third mode of vibration would have a frequency of 1265.92 Hz and would require the rod to be clamped at 1/3 of its length from one end.

I hope this helps to clarify the concepts of fundamental frequency and standing waves. Remember to always use the correct values for parameters and consider the different modes of vibration when calculating frequencies for standing waves.