(a)(i) what is resonance? (ii) State two eXwilples of resonance. (iii) Differentiate between loudness and intensity of sound. (b) When a ray is refracted th...
(iii) Differentiate between loudness and intensity of sound.
(b) When a ray is refracted through a rectangular glass prism, which of the following properties of the ray will change? Wavelength, frequency and speed.
(c)
(i) Copy the diagram above in your answer booklet.
(iii) On the copied diagram, sketch the pattern of the waves immediately after passing through the opening.
(d) A diverging lens of focal length 18.0 in is used to view a shark that is 90.0 in away from the lens. If the image formed is 1.0 m long, calculate the:
(i) image distance;
(ii) length of the shark.
(a)(i) Resonance. Resonance occurs when a body is set into vibration by a periodic force (or by impulses from a nearby vibrating body) whose frequency equals the natural frequency of the body, so that the body vibrates with maximum (very large) amplitude.
(a)(ii) Two examples of resonance.
The loud sound produced when the vibrating prongs of a tuning fork are held over an air column (resonance tube) whose length is adjusted until the sound is loudest.
A bridge vibrating strongly when soldiers march across it in step at a frequency equal to the natural frequency of the bridge (sympathetic vibration).
(a)(iii) Loudness versus intensity of sound. Intensity is a measurable physical quantity: the sound energy flowing per second through unit area held perpendicular to the direction of travel (unit \(\text{W m}^{-2}\)); it depends only on physical quantities (energy, time and area). Loudness is the physiological sensation produced in the ear by the sound; it depends on the intensity but also on the sensitivity and response of the individual ear, so it is subjective and not directly measurable.
(b) Refraction through a rectangular glass prism. When light passes from air into glass, the speed changes (it decreases) and the wavelength changes (it decreases in the same ratio). The frequency does not change. So: speed changes, wavelength changes, frequency unchanged.
(c) Diffraction through the wide opening. The given diagram shows straight (plane) wavefronts, drawn as parallel vertical lines, travelling towards a barrier that has a wide opening. Because the width of the opening is much larger than the wavelength, the wavefronts emerging on the far side remain almost straight and parallel across the middle of the gap, and only curve (bend) slightly round the two edges of the opening. The required sketch of the pattern immediately after passing through the opening is shown below.
Wavefronts passing through a wide opening: the emerging waves stay almost straight across the gap and curve only at the two edges.
(If the opening were instead made very narrow, comparable with the wavelength, the emerging waves would spread out strongly as almost circular arcs.)
(d) Diverging lens forming the image of a shark. Data: focal length \(f = -18.0\ \text{cm}\) (negative for a diverging lens), object distance \(u = 90.0\ \text{cm}\), image length \(= 1.0\ \text{m}\).
(d)(i) Image distance. Using the lens formula with \(f\) negative for a diverging lens:
The image distance is \(15\ \text{cm}\); the negative sign shows the image is virtual, upright and on the same side as the object, as expected for a diverging lens.
(d)(ii) Length of the shark. The magnification links the image and object sizes to their distances:
\[ m = \left|\frac{v}{u}\right| = \frac{\text{length of image}}{\text{length of shark}} \]\[ \text{length of shark} = \frac{\text{length of image} \times u}{|v|} = \frac{1.0 \times 90}{15} = 6.0\ \text{m} \]
(a)(i) Resonance. Resonance occurs when a body is set into vibration by a periodic force (or by impulses from a nearby vibrating body) whose frequency equals the natural frequency of the body, so that the body vibrates with maximum (very large) amplitude.
(a)(ii) Two examples of resonance.
The loud sound produced when the vibrating prongs of a tuning fork are held over an air column (resonance tube) whose length is adjusted until the sound is loudest.
A bridge vibrating strongly when soldiers march across it in step at a frequency equal to the natural frequency of the bridge (sympathetic vibration).
(a)(iii) Loudness versus intensity of sound. Intensity is a measurable physical quantity: the sound energy flowing per second through unit area held perpendicular to the direction of travel (unit \(\text{W m}^{-2}\)); it depends only on physical quantities (energy, time and area). Loudness is the physiological sensation produced in the ear by the sound; it depends on the intensity but also on the sensitivity and response of the individual ear, so it is subjective and not directly measurable.
(b) Refraction through a rectangular glass prism. When light passes from air into glass, the speed changes (it decreases) and the wavelength changes (it decreases in the same ratio). The frequency does not change. So: speed changes, wavelength changes, frequency unchanged.
(c) Diffraction through the wide opening. The given diagram shows straight (plane) wavefronts, drawn as parallel vertical lines, travelling towards a barrier that has a wide opening. Because the width of the opening is much larger than the wavelength, the wavefronts emerging on the far side remain almost straight and parallel across the middle of the gap, and only curve (bend) slightly round the two edges of the opening. The required sketch of the pattern immediately after passing through the opening is shown below.
Wavefronts passing through a wide opening: the emerging waves stay almost straight across the gap and curve only at the two edges.
(If the opening were instead made very narrow, comparable with the wavelength, the emerging waves would spread out strongly as almost circular arcs.)
(d) Diverging lens forming the image of a shark. Data: focal length \(f = -18.0\ \text{cm}\) (negative for a diverging lens), object distance \(u = 90.0\ \text{cm}\), image length \(= 1.0\ \text{m}\).
(d)(i) Image distance. Using the lens formula with \(f\) negative for a diverging lens:
The image distance is \(15\ \text{cm}\); the negative sign shows the image is virtual, upright and on the same side as the object, as expected for a diverging lens.
(d)(ii) Length of the shark. The magnification links the image and object sizes to their distances:
\[ m = \left|\frac{v}{u}\right| = \frac{\text{length of image}}{\text{length of shark}} \]\[ \text{length of shark} = \frac{\text{length of image} \times u}{|v|} = \frac{1.0 \times 90}{15} = 6.0\ \text{m} \]
