Goal: To understand sound Objectives: To learn about Sound waves To understand the Speed of sound To learn about Doppler Shifts To learn about Resonance

Sound waves What type of wave is a sound wave?

Compression Since sound is the compression of a material, sound is a Longitudinal wave (compression wave). You compress the material (in our case air) at some rate (so you compress the air some # of times per second), and this comes out as a pitch. This is usually created from the in and out vibrations of an object which causes the compression of air. The pitch is how often the object vibrates.

Speed of Sound In air at room temperature sound travels about 340 m/s. So, if the lightning strike is about 1 mile away it will take about 4.5 seconds for you to hear the “ka-boom”. However, the speed of sound depends on temperature. At 32 F the speed is 330 m/s. It also depends on the medium. In water the speed of sound can be 1500 m/s.

Quick sample A rock hits the bottom of a cliff that is 50 m high. If the speed of sound is 340 m/s how long will it take for you to hear the impact? HW note, you will have to find the time it takes the rock to fall to the bottom also.

Energy Sound waves have energy. A large enough “boom” can be felt, and not just heard. The energy of sound is given as a decibel level – which is an exponential scale. If the sound has enough energy, it can harm your eardrums. If even stronger it can break windows.

Decibel Scale I = power / area = P / (4π r2) Β = 10 dB * log10(I / Io) Io = 1 * 10-12 W/m2 Example: A 20 W speaker outputs its max power of sound. From a distance of 4 m away find: A) The intensity of sound B) The decibel level of the sound

Quick math note: 10(B / 10 dB) = I / Io So, if you have to solve for I for some reason (to then solve for a distance), you will have to use this trick

Doppler Shift (day 2) When a source of waves moves you have what is called a Doppler shift. Think to when you are creating a wave. The front part of the wave will move away from you at some constant wave speed. However, the position of the end of the wave depends on where you are when you FINISH the wave. So, if you move forward, the wave will be shortened. If you move backwards the wave will be lengthened. The amount of the change of the wave will just depend on how far you move in the time that it takes to make the wave.

Doppler equation So, the equations are: λ Obs = λ Emit * [(Vwave – Vsource)/ (Vwave - Vobserver) ] fo = fs * [(Vwave - Vobserver) / (Vwave – Vsource)] NOTE: You do have to watch direction!!! If the sound is traveling opposite to the direction of one of the 2 then you have to make that velocity negative.

Train/Indy Car Imagine a train or an Indy car moving towards you. While it moves towards you any noise it makes is “blue-shifted” – which means it goes to higher frequency (shorter wavelength means higher frequency). Once it passes you it is moving away from you, so the noise is then “red-shifted” – which means it goes to lower frequency.

Example A police officer chases a speeder. The siren from the officer at rest would have a frequency of 250 Hz. The cop is traveling at 50 m/s forward The speeder is traveling 45 m/s forward Find the frequency that the speeder observes.

Doppler shift and reflection Here you will get a double Doppler shift First you find the frequency the reflected object gets. That will be the reflected frequency The reflected frequency will be Doppler shifted again. However this time the source and the observer switch places and velocities switch sign as the wave is traveling in the opposite direction.

Example if time permits A fruit bat flies at 17 m/s towards a tree. If the bat emits a 22,000 Hz pulse towards the tree then find (assuming speed of sound is 340 m/s): A) The frequency the tree gets B) The frequency that the tree “emits” from the reflection C) The frequency the bat gets back

Resonance If a waves moves an integer number of wavelengths moving down and back this will create resonance. The waves going out will add to the ones coming in. Since the reflected and incoming waves will be in phase they will add to become a bigger wave.

Conclusion Sound is a compression wave Like properties of waves, sound obeys all of those properties, and does NOT travel in space. We have learned how to use the Doppler shift equations We have examined resonance