Have you ever wondered why larger musical instruments, like cellos, have a lower pitch than smaller instruments, like violins? This size-pitch relationship is caused by resonance, which refers to an object’s ability to oscillate with larger amplitudes at certain frequencies (National Science Foundation, 2023). Each object has its own resonant frequency: the frequency at which the object can oscillate with the greatest possible amplitude, given its physical characteristics (Brubaker, 2022). The physical characteristics that influence resonant frequency include length, thickness, tension, and material. For example, a violin’s strings are manufactured specifically so that when the bow moves across the four strings, they will vibrate at 196, 294, 440, and 660 Hz to produce the pitches G3, D4, A4, and E5 respectively (Jansson, 1990).
Just like musical instruments, buildings and the type of rock upon which they are built also have resonant frequencies, and this can become quite an interesting issue when dealing with earthquakes. Different types of rock have differing resonant frequencies; for example, bedrock has much higher resonant frequencies than ground made of soft sediments (National Science Foundation, 2023). Similarly, shorter buildings have a much higher resonant frequency than tall buildings. If the resonant frequency of the building matches that of the ground, when seismic activity occurs, it causes the ground and building to vibrate at their shared resonant frequency (Sbarra, et al., 2015; Chen, et al., 2015). Since resonant frequency means that the objects are vibrating with the highest possible amplitude, this can result in severe damage to the building.
The effects of matching resonant frequencies between buildings and their rock foundation were quite visible in the 2015 Gorkha earthquake in Nepal (Figure 1). During the earthquake, the ground shook for over 60 seconds, with approximately a 4-second period in the Kathmandu Valley: an area composed of soft soil deposits (Bhandary, Paudyal, and Okamura, 2021). The resonant frequencies most prominent in the Kathmandu Valley range from 0.300–0.488 Hz, which directly affect buildings with a resonant frequency of 3 to 5 seconds (Yamada, et al., 2016); specifically, seven- to nine-story buildings like the Dharahara Tower, a significant military watch tower (Figure 2) (Nepal Traveller, 2023). While the majority of the tall buildings throughout the valley were damaged, short buildings were only impacted in specific areas of the valley, along the edges. This was due to the inherent shape of the valley, which created higher frequencies in these areas that matched the resonant frequencies of the shorter structures (Bhandary, Paudyal, and Okamura, 2021).
Figure 1: This map differentiates the various areas of perceived shaking in the 2015 Gorkha earthquake in Nepal (Rafferty, 2023).
Figure 2: The 62-metre tall Dharahara Tower before and after the Gorkha earthquake (Sumner, 2015).
It is crucial that resonant frequencies of the ground are taken into account when designing new buildings. Due to the significance of resonant frequencies, the most ideal way to avoid major destruction of urban areas during earthquakes is to construct buildings with resonant frequencies that differ from that of the underlying rock.
References
Bhandary, N.P., Paudyal, Y.R. and Okamura, M., 2021. Resonance effect on shaking of tall buildings in Kathmandu Valley during the 2015 Gorkha earthquake in Nepal. Environmental Earth Sciences, 80(13), p.459. https://doi.org/10.1007/s12665-021-09754-9.
Brubaker, B., 2022. How the Physics of Resonance Shapes Reality. [online] Quanta Magazine. Available at: <https://www.quantamagazine.org/how-the-physics-of-resonance-shapes-reality-20220126/> [Accessed 28 October 2023].
Chen, S., Liu, Q., Zhai, C. and Wen, W., 2022. Influence of building-site resonance and building properties on site-city interaction: A numerical investigation. Soil Dynamics and Earthquake Engineering, 158, p.107307. https://doi.org/10.1016/j.soildyn.2022.107307.
Jansson, E.V., 1990. Experiments with the violin string and bridge. Applied Acoustics, 30(2–3), pp.133–146. https://doi.org/10.1016/0003-682X(90)90042-S.
National Science Foundation, 2023. Building Resonance: Structural stability during earthquakes- Incorporated Research Institutions for Seismology. [online] Available at: <https://www.iris.edu/hq/inclass/animation/building_resonance_the_resonant_frequency_of_different_seismic_waves> [Accessed 3 November 2023].
Nepal Traveller, 2023. Dharahara: A Tower of Resilience and Heritage in Nepal. [online] Available at: <https://nepaltraveller.com/sidetrack/dharahara-a-tower-of-resilience-and-heritage-in-nepal> [Accessed 3 November 2023].
Rafferty, J.P., 2023. Nepal Earthquake of 2015. [online] Available at: <https://www.britannica.com/topic/Nepal-earthquake-of-2015> [Accessed 10 November 2023].
Sbarra, P., Fodarella, A., Tosi, P., Rubeis, V.D. and Rovelli, A., 2015. Difference in shaking intensity between short and tall buildings: Known and new findings. Bulletin of the Seismological Society of America, 105(3), pp.1803–1809. https://doi.org/10.1785/0120140341.
Sumner, T., 2015. Nepal quake’s biggest shakes relatively spread out. [online] Available at: <https://www.sciencenews.org/article/nepal-quakes-biggest-shakes-relatively-spread-out> [Accessed 29 October 2023].
Yamada, M., Hayashida, T., Mori, J. and Mooney, W.D., 2016. Building damage survey and microtremor measurements for the source region of the 2015 Gorkha, Nepal, earthquake. Earth, Planets and Space, 68(1), p.117. https://doi.org/10.1186/s40623-016-0483-4.