Calculating Frequency of a Tuning Fork & Exploring Its Resonance

[Timiop2008]

A tuning fork oscillates with simple harmonic motion described the equation:

x = 0.00150cos(2770t) (where t is seconds)

a) calculate the frequency in Hz of the tuning fork

b) Suggest why only this tuning fork (taken from a set of 10 forks) gets louder when held above a glass bottle full of milk.

I don't know how to go about this question. Any help greatly appreciated.

 

[fluidistic]

A tuning fork oscillates with simple harmonic motion described the equation:

x = 0.00150cos(2770t) (where t is seconds)

a) calculate the frequency in Hz of the tuning fork

b) Suggest why only this tuning fork (taken from a set of 10 forks) gets louder when held above a glass bottle full of milk.

I don't know how to go about this question. Any help greatly appreciated.

A look at http://en.wikipedia.org/wiki/Simple_harmonic_motion, especially at the first formula encountered, will give you the straightforward answer.

 

[kerimek]

a) To calculate the frequency of the tuning fork, we can use the equation f = 1/T, where f is the frequency in Hz and T is the period in seconds. The period can be found by taking the inverse of the angular frequency, which is given by ω = 2πf. In this case, ω = 2770 rad/s, so T = 1/2770 s. Plugging this into the equation for frequency, we get: f = 1/(1/2770) = 2770 Hz.

b) The reason why this particular tuning fork may get louder when held above a glass bottle full of milk is due to resonance. Resonance occurs when an object is forced to vibrate at its natural frequency by an external force. In this case, the milk in the glass bottle may be acting as a resonator for the tuning fork, amplifying the sound waves produced by the fork. This could be due to the properties of milk, such as its density and viscosity, which may allow for better conduction and amplification of sound. It is also possible that the size and shape of the glass bottle may be causing a standing wave to form, further amplifying the sound produced by the tuning fork. It is important to note that not all materials will exhibit resonance with the tuning fork, which is why only this particular tuning fork may get louder when held above the glass bottle of milk.