2Power transmitted in a wave Sinusoidal wave on a stringWave IntensityInverse Square LawThe decibel scale
3Example CalculationOne end of a 10m-long rope is attached to a post, and pulled taut, to a tension of 140N. If the mass of the rope is 800g, what is the speed of transverse waves on the rope?If the free end of the rope is waggled up and down with a frequency of 1.2Hz, what is the wavelength of the transverse waves on the rope?
4Energy in Wave Motion Waves transport energy. Examples?? How can we quantify this??
5Wave on a string A Consider force in y-direction at point A on string: TyyConsider force in y-direction at point A on string:x
6Wave on a string If a force F acts to move an object with velocity v: Rate of energy transfer (power) = F• v =Fv for F//vSo for our wave on a string, P = Tyv……………..ieConsider case for sinusoidal wave………………
8Sinusoidal Wave on a string NB, for all MECHANICAL waves, Pave A22
9Example CalculationA piano wire with mass 3g and length 80cm is stretched with a tension of 25N. A wave with frequency 120Hz and amplitude 1.6mm travels along the wire.Calculate the average power carried by the waveWhat happens to the average power if the wave amplitude is halved?
10Wave IntensityIntensity I : Average rate at which energy is transported by the wave through unit surface area perpendicular to direction of propagation(average power per unit area)For waves spreading out equally in three dimensions from a point source, the power at distance r is distributed evenly over a sphere of radius r, surface area 4r
12Example Calculation(a) For the piano in the previous question, calculate the sound intensity at a distance of 5m(b) How much does the sound intensity decrease if you move to a distance of 15m from the piano?
13The decibel scaleUsed to provide a logarithmic scale for comparison of 2 quantities.Often (but not only) used for sound intensities:
14ExamplesWhat is the attenuation in dB of the sound intensity heard by a listener when they move from an initial distance of 3m to a final distance of 24m from the source?An electronic amplifier increases the amplitude of an AC signal from 10mV to 5V. What is the gain in dB of the amplifier?
15Sound IntensitiesThe dB scale is often used as an “absolute” measure of sound intensity (loudness)(eg the average sound intensity for traffic on the M1 is 75dB, or whatever)Here, the intensity is measured relative to the threshold of human hearing:I0 = W/m2