3 The ray diagram at right represents a periodic water wave

3. The ray diagram at right represents a periodic water wave at the boundary between two different media (i.e., two regions of different depth in a large tank of water). The wave is generated by a dowel moving back and forth at a steady rate. Region 1 Region 2 Does the propagation speed of the transmitted wave (in region 2) depend on the propagation speed of the incident wave (in region 1)? Explain. a. Is it possible to increase the propagation speed of the transmitted propagation speed of the incident wave? If so, explain how (e.g., by and forth faster or by changing the depth of water in region 1). If not, explain why not. wave by changing the moving the dowel back b. Does the frequency of the transmitted wave depend on the frequency of the incident wa Explain. ve? Is it possible to increase the frequency of the transmitted wave without changing the frequency of the incident wave? If so, explain how. If not, explain why no

Solution

3) a)

let the refractive index of the medium be n

then speed of the transmitted wave = speed of incident wave / n

therefore yes speed of the transmitted wave depends on  speed of incident wave

if speed of incident wave increases the transmitted wave also increases

b)YES frequency of transmitted wave = frequency of incident wave

no it is not as frequency of a wave does not depend on medium charecteristics

c)

if we decrease the frequency of incident wave we increase the wavelength of incident wave since

frequency is inversely proportional to wavelength

as we increase the wavelength of incident wave we increase the wavelength of transmitted wave

if we increase propagation speed of incident wave we increase the propagation speed of transmitted wave

since frequency remains constant wavelength of transmitted wave increases.

d) Yes

according to snells law sin i / sin r = n

so if i changes keeping n constant r changes