The existence of longitudinal waves in vibrating piano strings has been previously established, as has their importance in producing the characteristic sound of the piano. Modeling of the coupling between the transverse and longitudinal motion of strings indicates that the amplitude of the longitudinal waves are quadratically related to the transverse displacement of the string, however, experimental verification of this relationship is lacking. In the work reported here this relationship is tested by driving the transverse motion of a piano string at only two frequencies, which simplifies the task of unambiguously identifying the constituent signals. The results indicate that the generally accepted relationship between the transverse motion and the longitudinal motion is valid. It is further shown that this dependence on transverse displacement is a good approximation when a string is excited by the impact of the hammer during normal play.
It is known that longitudinal waves in piano strings noticeably contribute to the characteristic sound of the instrument. These waves can be induced by directly exciting the motion with a longitudinal component of the piano hammer, or by the stretching of the string associated with the transverse displacement. Longitudinal waves that are induced by the transverse motion of the string can occur at frequencies other than the longitudinal resonance frequencies, and the amplitude of the waves produced in this way are believed to vary quadratically with the amplitude of the transverse motion. We present the results of an experimental investigation that demonstrates the quadratic relationship between the magnitude of the longitudinal waves and the magnitude of the transverse displacement for steady-state, low-amplitude excitation. However, this relationship is only approximately correct under normal playing conditions.
The Himalayan singing bowl is a nearly symmetric idiophone played by rotating a wooden stick called a puja around the outer rim of the bowl. The vibrations of the bowl are excited by a stick-slip mechanism, which produces a radial motion of the bowl with a deflection shape similar to the (2,0) mode. We present experimental evidence that the position of the puja coincides with the point of minimum displacement on the bowl, indicating that it imposes a node in the deflection shape that rotates around the bowl with the puja. However, in many cases the puja is forced off of the bowl and an audible chatter is produced as the puja repeatedly strikes the bowl several times per second. This indicates that the position of the puja is not a node, but rather merely a point of minimum deflection. Examination of high-speed electronic speckle pattern interferograms and time-resolve acoustic spectra provide insight into the mechanics of the singing bowl and the origin of the chatter.
A simple demonstration that is occasionally used in the classroom to show that light carries momentum involves making an orchestral cymbal audibly ring using light from a common photoflash. A metal plate or a piece of foil can also be used; however, it appears that many people use a cymbal because the sound is easily heard at a reasonable distance. It is such an impressive example of the effects attributable to photon momentum that it is posted on the CERN website for educational resources under the name “singing cymbal.” Although it is an impressive demonstration, a series of simple classroom experiments can show that the sound of the singing cymbal is not due to the transfer of photon momentum.
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