Superposition 1. A pipe that is 120 cm long resonates to produce sound of wavelengths 480 cm, 160 cm, and 96 cm but does not resonate at any wavelengths longer than these. This pipe is A) open at both ends. B) open at one end and closed at the other end. C) closed at both ends. D) We cannot tell because we do not know the frequency of the sound. 2. A thin 2.00-m string of mass 50.0 g is fixed at both ends and under a tension of 70.0 N. If it is set into small-amplitude oscillation, what is the frequency of the first harmonic mode? A) 6.61 Hz B) 13.2 Hz C) 26.5 Hz D) 52.9 Hz5. The picture below shows two pulses approaching each other on a stretched string at time t = 0 s. Both pulses have a speed of 1.0 m/s. Using the empty graph axes below the picture, draw a picture of the string at t = 4 s. D (cm) 2 - . . 1=05 1 - 10m/'s 1.0 m/s 12 16 18 20 x (m) D (cm) 12 x (m) Wave optics 6. The figure below shows the viewing screen in a double-slit experiment. Fringe C is the central maximum. What will happen to the fringe spacing if (a) The wavelength of the light is decreased? (b) The spacing between the slits is decreased? (c) The distance to the screen is decreased? B D E3. Two strings with linear densities of 5.0 g/m are stretched over pulleys, adjusted to have vibrating lengths of 50 cm, and attached to hanging blocks. The block attached to string 1 has a mass of 20 kg and the block attached to wire 2 has mass M. Listeners hear a beat frequency of 2.0 Hz when wire 1 is excited at its fundamental frequency and wire 2 at its third harmonic. What is one possible value for mass M? String 1 50 cm 20 kg O String 2 M 4. Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 20 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 60 cm. a. What is the wavelength of the sound? b. If the distance between the speakers continuew to increase, at what separation will the sound intensity again be maximum.10. Given figure shows the light intensity on a screen behind a double slit. The slit spacing is 0.20 mm and the wavelength of the light is 620 nm. What is the distance from the slits to the screen? [Ans- 167 cm] Intensity (mW/m) 12- y x (cm) 2.0 cmB C D E 7. In a single-slit experiment, the slit width is 200 times the wavelength of the light. What is the width (in mm) of the central maximum on a screen 2.0 m behind the slit? 8. A diffraction grating produces a first-order maximum at an angle of 20. What is the angle of the second-order maximum? 9. A diffraction grating is placed 1.00 m from a viewing screen. Light from a hydrogen lamp is passed through the grating, and the 656-nm-wavelength emission line in the hydrogen spectrum is seen 60.0 cm to one side of the center. Then the hydrogen lamp is replaced with . a mercury lamp. a. Where does the 546-nm-wavelength emission line in the mercury spectrum fall on the screen? b. A spectral line is seen on the screen 36.4 cm away from the center. What is the wavelength